夏日晨起天光好，微風吹花氣味佳，忽而 眼 皮直跳，不知是何兆？欲法 梅 花心易，急讀《   》觀水之法︰

……

，  眼為離 ䷝ 目，左通心，其跳吉。跳者 眉居離眼上，或是喜上眉梢之兆。剛過夏至日，兆體取為乾 ䷀ ，目離變二爻，眉梢動上爻，樹欲靜，風不止，定前後。蓋指夬 ䷪ 之革 ䷰ ，當是『己日乃革』，『君子豹變』之象。

因是速往學堂。剛上迴廊，就見課堂外擺著桌子，三五同學看到我來，忙向前導引桌前，在那『未曾有』的『簽到簿』上 畫 卯，還得『工筆』寫句『勵志』語，只覺興筆寫下

 

，卻瞧見同學搔首笑說︰這可是句 『畫』。趕緊添補上一筆

學而時習之不亦悅乎。

一進教室大吃一驚，桌子圍成了『圓』，拱著講桌而排，中央拼作『方』，上有派生碼訊，正播放著學習日子裡的點點滴滴，甚至還配著音樂呢！？一時如在夢中，以為今兒已經是『禮拜一』了，將要開『同樂會』？？正惶惑間，……學長走進了教室

派︰同學們，大家好。【彷彿一點都不驚訝】

今天的課堂佈置，嗯！天圓而地方，這可不是那『孔方』，擺明了要『化緣』，也罷！！請這兩位同學，出外跑一遭，將『下』星期一才辦的 同樂會，先行個籌備會，排演一番。在此等

『吃』的之際，正好回顧彼此相聚的短暫時光。…

沒多久，大家的桌上，擺著各樣點心、糖果、飲料，零零種種的有一整桌。祇聽學長講︰今兒，出『錢』的與出『力』的都不講課，大家都來『聽』課，聽 M♪o 講這學期的『最後一堂課』。………【熱烈鼓掌，久久不歇】

原來是學長帶頭『作怪』，看來不上『講台』，這掌聲是不會歇的了。

─── 《M♪O 之學習筆記本《巳》文章︰【䷪】有戎勿恤》

 

既已知道一顆『小馬達』的『電路模型』，正好乘著

Modular Circuits

Andras Tantos

Motor Modeling

………

 

文字

A Practical Example: the R/C Car

But just how useful this model is? To be honest not terribly, as you rarely use a motor without anything connected to it. Modeling the mechanical properties of just the motor is not that practical. Luckily, the same model can be used for a wide range of applications, for example for moving platforms.

In this example, I’ll dust of my old Tumbleweed robot. It is based on a Stampede R/C car. A first-level mechanical model is fairly simple for this kind of platform: the motor through a number of gears, drives a wheel, which than moves the whole body.

From the motors perspective, it looks as if it moves the whole weigh of the car as if it was spread around the circumference of the wheel. The gears can be simplified into a single gear-box with a ratio on ‘1:N’, and we can further assume that the inertia of the gears are negligible compared to the inertia of the other components. With this, we get to the following model:

 

Here, the motor is represented by our usual model of a lossy rotating disc (parameters with the ‘m’ suffix), and our load is represented by another lossy rotating disc of the same kind (parameters with the ‘w’ suffix).

The new component is the gear-box, so let’s talk about it first! Gears work as torque-speed-converters. They multiply the torque by ‘N’ and reduce the speed by a factor of ‘N’:

T_w = T_m*N
s_w = s_m/N

We have our previous equations for the torques ‘consumed’ by a disc and the draw from before:

T_dw= f_w and T_Jw= J_w * (ds_w/dt)

Putting s_m into these equations we get:

T_dw= f_w and T_Jw= J_w/N * (ds_m/dt)

Now, from the motors’ perspective, it only sees 1/N-th of this torque through the gear-box (remember, gear-boxes convert torque). So the torque of these components expressed on the motor-end of the gear-box are:

T_dm= 1/N *f_w and T_Jm= 1/N² * J_w * (ds_m/dt)

It looks like our components kept their properties, but their effect shrunk. So, now that we’ve eliminated the gear-box, we ended up with the following model:

 

This can be further simplified, by combining the two discs and the two frictions into one of each:

 

And now, we’re back to the previous model: a single disc and a single friction. We just have more complex equations for calculating the values. Of course this also means that the equivalent circuit will be identical as well, except that the values of the current-source and the capacitance are now a little more complex:

I_f = (f_m+f_w/N)/K_r

and

C = (J_m+J_w/N²)/(K_E*K_T)

A further simplification can be made as well: we can say that the inertia of the motor is negligible compared to the inertia of the whole body (even after the gear-conversion). That results in a further simplified capacitor model:

C = (J_w/N²)/(K_E*K_T)

 

羽翼，回到《運動學》耶？！

重新認識『小齒輪』之機械優點也！？

Gear

Two meshing gears transmitting rotational motion. Note that the smaller gear is rotating faster. Since the larger gear is rotating less quickly, its torque is proportionally greater. One subtlety of this particular arrangement is that the linear speed at the pitch diameter is the same on both gears.

 

A gear or cogwheel is a rotating machine part having cut like teeth, or cogs, which mesh with another toothed part to transmit torque. Geared devices can change the speed, torque, and direction of a power source. Gears almost always produce a change in torque, creating a mechanical advantage, through their gear ratio, and thus may be considered a simple machine. The teeth on the two meshing gears all have the same shape.^[1] Two or more meshing gears, working in a sequence, are called a gear train or a transmission. A gear can mesh with a linear toothed part, called a rack, producing translation instead of rotation.

The gears in a transmission are analogous to the wheels in a crossed, belt pulley system. An advantage of gears is that the teeth of a gear prevent slippage.

When two gears mesh, if one gear is bigger than the other, a mechanical advantage is produced, with the rotational speeds, and the torques, of the two gears differing in proportion to their diameters.

In transmissions with multiple gear ratios—such as bicycles, motorcycles, and cars—the term “gear” as in “first gear” refers to a gear ratio rather than an actual physical gear. The term describes similar devices, even when the gear ratio is continuous rather than discrete, or when the device does not actually contain gears, as in a continuously variable transmission.^[2]